Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,2,Mod(107,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([3, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.p (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.79289409601\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{12})\) |
Coefficient field: | 16.0.11007531417600000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 7x^{12} + 48x^{8} - 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 293.3 | ||
Root | \(-0.596975 - 0.159959i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 475.293 |
Dual form | 475.2.p.g.107.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.15988 | − | 0.578737i | 1.52726 | − | 0.409229i | 0.605138 | − | 0.796121i | \(-0.293118\pi\) |
0.922125 | + | 0.386892i | \(0.126451\pi\) | |||||||
\(3\) | −0.0988601 | − | 0.368951i | −0.0570769 | − | 0.213014i | 0.931497 | − | 0.363748i | \(-0.118503\pi\) |
−0.988574 | + | 0.150734i | \(0.951836\pi\) | |||||||
\(4\) | 2.59808 | − | 1.50000i | 1.29904 | − | 0.750000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.427051 | − | 0.739674i | −0.174343 | − | 0.301971i | ||||
\(7\) | 1.22474 | − | 1.22474i | 0.462910 | − | 0.462910i | −0.436698 | − | 0.899608i | \(-0.643852\pi\) |
0.899608 | + | 0.436698i | \(0.143852\pi\) | |||||||
\(8\) | 1.58114 | − | 1.58114i | 0.559017 | − | 0.559017i | ||||
\(9\) | 2.47172 | − | 1.42705i | 0.823908 | − | 0.475684i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.85410 | −0.559033 | −0.279516 | − | 0.960141i | \(-0.590174\pi\) | ||||
−0.279516 | + | 0.960141i | \(0.590174\pi\) | |||||||
\(12\) | −0.810272 | − | 0.810272i | −0.233905 | − | 0.233905i | ||||
\(13\) | −1.79092 | − | 0.479877i | −0.496713 | − | 0.133094i | 0.00176097 | − | 0.999998i | \(-0.499439\pi\) |
−0.498474 | + | 0.866905i | \(0.666106\pi\) | |||||||
\(14\) | 1.93649 | − | 3.35410i | 0.517549 | − | 0.896421i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 0.171231 | + | 0.639042i | 0.0415295 | + | 0.154990i | 0.983577 | − | 0.180490i | \(-0.0577682\pi\) |
−0.942047 | + | 0.335480i | \(0.891102\pi\) | |||||||
\(18\) | 4.51273 | − | 4.51273i | 1.06366 | − | 1.06366i | ||||
\(19\) | 4.33013 | − | 0.500000i | 0.993399 | − | 0.114708i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.572949 | − | 0.330792i | −0.125028 | − | 0.0721848i | ||||
\(22\) | −4.00463 | + | 1.07304i | −0.853790 | + | 0.228772i | ||||
\(23\) | −1.34486 | + | 5.01910i | −0.280423 | + | 1.04655i | 0.671696 | + | 0.740827i | \(0.265566\pi\) |
−0.952119 | + | 0.305727i | \(0.901100\pi\) | |||||||
\(24\) | −0.739674 | − | 0.427051i | −0.150985 | − | 0.0871714i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.14590 | −0.813077 | ||||||||
\(27\) | −1.58114 | − | 1.58114i | −0.304290 | − | 0.304290i | ||||
\(28\) | 1.34486 | − | 5.01910i | 0.254155 | − | 0.948520i | ||||
\(29\) | 0.330792 | + | 0.572949i | 0.0614266 | + | 0.106394i | 0.895103 | − | 0.445859i | \(-0.147102\pi\) |
−0.833677 | + | 0.552253i | \(0.813768\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.47935i | 0.265699i | 0.991136 | + | 0.132849i | \(0.0424127\pi\) | ||||
−0.991136 | + | 0.132849i | \(0.957587\pi\) | |||||||
\(32\) | −1.73621 | + | 6.47963i | −0.306922 | + | 1.14545i | ||||
\(33\) | 0.183297 | + | 0.684072i | 0.0319079 | + | 0.119082i | ||||
\(34\) | 0.739674 | + | 1.28115i | 0.126853 | + | 0.219716i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.28115 | − | 7.41517i | 0.713525 | − | 1.23586i | ||||
\(37\) | −6.86474 | − | 6.86474i | −1.12856 | − | 1.12856i | −0.990412 | − | 0.138144i | \(-0.955886\pi\) |
−0.138144 | − | 0.990412i | \(-0.544114\pi\) | |||||||
\(38\) | 9.06317 | − | 3.58594i | 1.47024 | − | 0.581717i | ||||
\(39\) | 0.708204i | 0.113403i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.92705 | + | 2.26728i | 0.613302 | + | 0.354090i | 0.774257 | − | 0.632872i | \(-0.218124\pi\) |
−0.160954 | + | 0.986962i | \(0.551457\pi\) | |||||||
\(42\) | −1.42894 | − | 0.382883i | −0.220490 | − | 0.0590802i | ||||
\(43\) | −3.10197 | + | 0.831171i | −0.473046 | + | 0.126752i | −0.487463 | − | 0.873144i | \(-0.662078\pi\) |
0.0144165 | + | 0.999896i | \(0.495411\pi\) | |||||||
\(44\) | −4.81710 | + | 2.78115i | −0.726205 | + | 0.419275i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 11.6190i | 1.71312i | ||||||||
\(47\) | 3.74101 | + | 1.00240i | 0.545683 | + | 0.146215i | 0.521121 | − | 0.853483i | \(-0.325514\pi\) |
0.0245623 | + | 0.999698i | \(0.492181\pi\) | |||||||
\(48\) | 0.368951 | + | 0.0988601i | 0.0532535 | + | 0.0142692i | ||||
\(49\) | 4.00000i | 0.571429i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.218847 | − | 0.126351i | 0.0306447 | − | 0.0176927i | ||||
\(52\) | −5.37277 | + | 1.43963i | −0.745070 | + | 0.199641i | ||||
\(53\) | −13.0131 | − | 3.48685i | −1.78748 | − | 0.478955i | −0.795570 | − | 0.605862i | \(-0.792828\pi\) |
−0.991915 | + | 0.126907i | \(0.959495\pi\) | |||||||
\(54\) | −4.33013 | − | 2.50000i | −0.589256 | − | 0.340207i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 3.87298i | − | 0.517549i | ||||||
\(57\) | −0.612552 | − | 1.54817i | −0.0811345 | − | 0.205061i | ||||
\(58\) | 1.04606 | + | 1.04606i | 0.137354 | + | 0.137354i | ||||
\(59\) | −7.13264 | + | 12.3541i | −0.928591 | + | 1.60837i | −0.142910 | + | 0.989736i | \(0.545646\pi\) |
−0.785681 | + | 0.618631i | \(0.787687\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.78115 | + | 8.28120i | 0.612164 | + | 1.06030i | 0.990875 | + | 0.134784i | \(0.0430341\pi\) |
−0.378711 | + | 0.925515i | \(0.623633\pi\) | |||||||
\(62\) | 0.856153 | + | 3.19521i | 0.108732 | + | 0.405792i | ||||
\(63\) | 1.27946 | − | 4.77501i | 0.161197 | − | 0.601594i | ||||
\(64\) | 13.0000i | 1.62500i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.791796 | + | 1.37143i | 0.0974634 | + | 0.168811i | ||||
\(67\) | 1.55291 | − | 5.79555i | 0.189719 | − | 0.708040i | −0.803852 | − | 0.594829i | \(-0.797220\pi\) |
0.993571 | − | 0.113211i | \(-0.0361135\pi\) | |||||||
\(68\) | 1.40343 | + | 1.40343i | 0.170191 | + | 0.170191i | ||||
\(69\) | 1.98475 | 0.238936 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.35410 | + | 1.93649i | 0.398059 | + | 0.229819i | 0.685646 | − | 0.727935i | \(-0.259520\pi\) |
−0.287587 | + | 0.957754i | \(0.592853\pi\) | |||||||
\(72\) | 1.65177 | − | 6.16451i | 0.194663 | − | 0.726494i | ||||
\(73\) | −11.4671 | + | 3.07261i | −1.34213 | + | 0.359622i | −0.857223 | − | 0.514946i | \(-0.827812\pi\) |
−0.484904 | + | 0.874567i | \(0.661145\pi\) | |||||||
\(74\) | −18.7999 | − | 10.8541i | −2.18544 | − | 1.26176i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 10.5000 | − | 7.79423i | 1.20443 | − | 0.894059i | ||||
\(77\) | −2.27080 | + | 2.27080i | −0.258782 | + | 0.258782i | ||||
\(78\) | 0.409864 | + | 1.52963i | 0.0464079 | + | 0.173197i | ||||
\(79\) | 6.80185 | − | 11.7812i | 0.765268 | − | 1.32548i | −0.174837 | − | 0.984597i | \(-0.555940\pi\) |
0.940105 | − | 0.340886i | \(-0.110727\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.85410 | − | 6.67550i | 0.428234 | − | 0.741722i | ||||
\(82\) | 9.79410 | + | 2.62432i | 1.08158 | + | 0.289808i | ||||
\(83\) | 10.5549 | + | 10.5549i | 1.15855 | + | 1.15855i | 0.984788 | + | 0.173762i | \(0.0555925\pi\) |
0.173762 | + | 0.984788i | \(0.444408\pi\) | |||||||
\(84\) | −1.98475 | −0.216554 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −6.21885 | + | 3.59045i | −0.670596 | + | 0.387169i | ||||
\(87\) | 0.178688 | − | 0.178688i | 0.0191574 | − | 0.0191574i | ||||
\(88\) | −2.93159 | + | 2.93159i | −0.312509 | + | 0.312509i | ||||
\(89\) | 1.27491 | + | 2.20820i | 0.135140 | + | 0.234069i | 0.925651 | − | 0.378379i | \(-0.123518\pi\) |
−0.790511 | + | 0.612448i | \(0.790185\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.78115 | + | 1.60570i | −0.291544 | + | 0.168323i | ||||
\(92\) | 4.03459 | + | 15.0573i | 0.420635 | + | 1.56983i | ||||
\(93\) | 0.545807 | − | 0.146248i | 0.0565975 | − | 0.0151653i | ||||
\(94\) | 8.66025 | 0.893237 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.56231 | 0.261514 | ||||||||
\(97\) | 8.27055 | − | 2.21609i | 0.839747 | − | 0.225010i | 0.186786 | − | 0.982401i | \(-0.440193\pi\) |
0.652962 | + | 0.757391i | \(0.273526\pi\) | |||||||
\(98\) | 2.31495 | + | 8.63950i | 0.233845 | + | 0.872722i | ||||
\(99\) | −4.58283 | + | 2.64590i | −0.460592 | + | 0.265923i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.85410 | − | 13.6037i | −0.781512 | − | 1.35362i | −0.931061 | − | 0.364865i | \(-0.881115\pi\) |
0.149548 | − | 0.988754i | \(-0.452218\pi\) | |||||||
\(102\) | 0.399558 | − | 0.399558i | 0.0395622 | − | 0.0395622i | ||||
\(103\) | −6.86474 | + | 6.86474i | −0.676403 | + | 0.676403i | −0.959184 | − | 0.282782i | \(-0.908743\pi\) |
0.282782 | + | 0.959184i | \(0.408743\pi\) | |||||||
\(104\) | −3.59045 | + | 2.07295i | −0.352073 | + | 0.203269i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −30.1246 | −2.92596 | ||||||||
\(107\) | 0.770867 | + | 0.770867i | 0.0745225 | + | 0.0745225i | 0.743386 | − | 0.668863i | \(-0.233219\pi\) |
−0.668863 | + | 0.743386i | \(0.733219\pi\) | |||||||
\(108\) | −6.47963 | − | 1.73621i | −0.623502 | − | 0.167067i | ||||
\(109\) | 7.54153 | − | 13.0623i | 0.722347 | − | 1.25114i | −0.237709 | − | 0.971336i | \(-0.576397\pi\) |
0.960057 | − | 0.279806i | \(-0.0902700\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.85410 | + | 3.21140i | −0.175984 | + | 0.304812i | ||||
\(112\) | 0.448288 | + | 1.67303i | 0.0423592 | + | 0.158087i | ||||
\(113\) | 8.71597 | − | 8.71597i | 0.819929 | − | 0.819929i | −0.166168 | − | 0.986097i | \(-0.553139\pi\) |
0.986097 | + | 0.166168i | \(0.0531395\pi\) | |||||||
\(114\) | −2.21902 | − | 2.98936i | −0.207830 | − | 0.279979i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.71885 | + | 0.992377i | 0.159591 | + | 0.0921399i | ||||
\(117\) | −5.11148 | + | 1.36962i | −0.472557 | + | 0.126621i | ||||
\(118\) | −8.25585 | + | 30.8113i | −0.760013 | + | 2.83641i | ||||
\(119\) | 0.992377 | + | 0.572949i | 0.0909710 | + | 0.0525222i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.56231 | −0.687482 | ||||||||
\(122\) | 15.1193 | + | 15.1193i | 1.36884 | + | 1.36884i | ||||
\(123\) | 0.448288 | − | 1.67303i | 0.0404207 | − | 0.150852i | ||||
\(124\) | 2.21902 | + | 3.84346i | 0.199274 | + | 0.345153i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | − | 11.0539i | − | 0.984759i | ||||||
\(127\) | 2.99254 | − | 11.1683i | 0.265545 | − | 0.991029i | −0.696370 | − | 0.717683i | \(-0.745203\pi\) |
0.961916 | − | 0.273346i | \(-0.0881305\pi\) | |||||||
\(128\) | 4.05116 | + | 15.1191i | 0.358075 | + | 1.33635i | ||||
\(129\) | 0.613323 | + | 1.06231i | 0.0540000 | + | 0.0935308i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.13525 | − | 15.8227i | 0.798151 | − | 1.38244i | −0.122668 | − | 0.992448i | \(-0.539145\pi\) |
0.920819 | − | 0.389990i | \(-0.127522\pi\) | |||||||
\(132\) | 1.50233 | + | 1.50233i | 0.130761 | + | 0.130761i | ||||
\(133\) | 4.69093 | − | 5.91567i | 0.406755 | − | 0.512954i | ||||
\(134\) | − | 13.4164i | − | 1.15900i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.28115 | + | 0.739674i | 0.109858 | + | 0.0634265i | ||||
\(137\) | −3.74101 | − | 1.00240i | −0.319616 | − | 0.0856410i | 0.0954440 | − | 0.995435i | \(-0.469573\pi\) |
−0.415060 | + | 0.909794i | \(0.636240\pi\) | |||||||
\(138\) | 4.28682 | − | 1.14865i | 0.364918 | − | 0.0977796i | ||||
\(139\) | −2.11111 | + | 1.21885i | −0.179062 | + | 0.103381i | −0.586852 | − | 0.809694i | \(-0.699633\pi\) |
0.407790 | + | 0.913076i | \(0.366300\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 1.47935i | − | 0.124584i | ||||||
\(142\) | 8.36516 | + | 2.24144i | 0.701989 | + | 0.188097i | ||||
\(143\) | 3.32056 | + | 0.889741i | 0.277679 | + | 0.0744039i | ||||
\(144\) | 2.85410i | 0.237842i | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −22.9894 | + | 13.2729i | −1.90261 | + | 1.09847i | ||||
\(147\) | 1.47580 | − | 0.395440i | 0.121722 | − | 0.0326154i | ||||
\(148\) | −28.1322 | − | 7.53800i | −2.31245 | − | 0.619620i | ||||
\(149\) | −8.40755 | − | 4.85410i | −0.688773 | − | 0.397664i | 0.114379 | − | 0.993437i | \(-0.463512\pi\) |
−0.803152 | + | 0.595774i | \(0.796846\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 4.69075i | − | 0.381728i | −0.981617 | − | 0.190864i | \(-0.938871\pi\) | ||
0.981617 | − | 0.190864i | \(-0.0611289\pi\) | |||||||
\(152\) | 6.05596 | − | 7.63710i | 0.491203 | − | 0.619451i | ||||
\(153\) | 1.33518 | + | 1.33518i | 0.107943 | + | 0.107943i | ||||
\(154\) | −3.59045 | + | 6.21885i | −0.289327 | + | 0.501129i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.06231 | + | 1.83997i | 0.0850525 | + | 0.147315i | ||||
\(157\) | 0.382883 | + | 1.42894i | 0.0305574 | + | 0.114042i | 0.979520 | − | 0.201347i | \(-0.0645318\pi\) |
−0.948963 | + | 0.315389i | \(0.897865\pi\) | |||||||
\(158\) | 7.87297 | − | 29.3823i | 0.626340 | − | 2.33753i | ||||
\(159\) | 5.14590i | 0.408096i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.50000 | + | 7.79423i | 0.354650 | + | 0.614271i | ||||
\(162\) | 4.46102 | − | 16.6488i | 0.350491 | − | 1.30805i | ||||
\(163\) | −1.22474 | − | 1.22474i | −0.0959294 | − | 0.0959294i | 0.657513 | − | 0.753443i | \(-0.271608\pi\) |
−0.753443 | + | 0.657513i | \(0.771608\pi\) | |||||||
\(164\) | 13.6037 | 1.06227 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 28.9058 | + | 16.6888i | 2.24352 | + | 1.29530i | ||||
\(167\) | 1.45405 | − | 5.42660i | 0.112518 | − | 0.419923i | −0.886571 | − | 0.462592i | \(-0.846919\pi\) |
0.999089 | + | 0.0426690i | \(0.0135861\pi\) | |||||||
\(168\) | −1.42894 | + | 0.382883i | −0.110245 | + | 0.0295401i | ||||
\(169\) | −8.28120 | − | 4.78115i | −0.637015 | − | 0.367781i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.98936 | − | 7.41517i | 0.763905 | − | 0.567053i | ||||
\(172\) | −6.81241 | + | 6.81241i | −0.519441 | + | 0.519441i | ||||
\(173\) | −1.17190 | − | 4.37358i | −0.0890977 | − | 0.332517i | 0.906961 | − | 0.421215i | \(-0.138396\pi\) |
−0.996059 | + | 0.0886977i | \(0.971730\pi\) | |||||||
\(174\) | 0.282530 | − | 0.489357i | 0.0214186 | − | 0.0370980i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.927051 | − | 1.60570i | 0.0698791 | − | 0.121034i | ||||
\(177\) | 5.26319 | + | 1.41027i | 0.395606 | + | 0.106002i | ||||
\(178\) | 4.03161 | + | 4.03161i | 0.302182 | + | 0.302182i | ||||
\(179\) | 9.06914 | 0.677859 | 0.338930 | − | 0.940812i | \(-0.389935\pi\) | ||||
0.338930 | + | 0.940812i | \(0.389935\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.2812 | − | 7.66788i | 0.987180 | − | 0.569949i | 0.0827501 | − | 0.996570i | \(-0.473630\pi\) |
0.904430 | + | 0.426622i | \(0.140296\pi\) | |||||||
\(182\) | −5.07767 | + | 5.07767i | −0.376382 | + | 0.376382i | ||||
\(183\) | 2.58269 | − | 2.58269i | 0.190918 | − | 0.190918i | ||||
\(184\) | 5.80948 | + | 10.0623i | 0.428280 | + | 0.741803i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.09424 | − | 0.631757i | 0.0802332 | − | 0.0463227i | ||||
\(187\) | −0.317479 | − | 1.18485i | −0.0232164 | − | 0.0866447i | ||||
\(188\) | 11.2230 | − | 3.00721i | 0.818525 | − | 0.219323i | ||||
\(189\) | −3.87298 | −0.281718 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.14590 | 0.517059 | 0.258530 | − | 0.966003i | \(-0.416762\pi\) | ||||
0.258530 | + | 0.966003i | \(0.416762\pi\) | |||||||
\(192\) | 4.79636 | − | 1.28518i | 0.346148 | − | 0.0927500i | ||||
\(193\) | −2.14607 | − | 8.00926i | −0.154478 | − | 0.576519i | −0.999150 | − | 0.0412344i | \(-0.986871\pi\) |
0.844672 | − | 0.535285i | \(-0.179796\pi\) | |||||||
\(194\) | 16.5808 | − | 9.57295i | 1.19043 | − | 0.687298i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.00000 | + | 10.3923i | 0.428571 | + | 0.742307i | ||||
\(197\) | −1.33518 | + | 1.33518i | −0.0951276 | + | 0.0951276i | −0.753069 | − | 0.657941i | \(-0.771427\pi\) |
0.657941 | + | 0.753069i | \(0.271427\pi\) | |||||||
\(198\) | −8.36706 | + | 8.36706i | −0.594621 | + | 0.594621i | ||||
\(199\) | −18.2945 | + | 10.5623i | −1.29686 | + | 0.748742i | −0.979860 | − | 0.199684i | \(-0.936008\pi\) |
−0.316999 | + | 0.948426i | \(0.602675\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.29180 | −0.161651 | ||||||||
\(202\) | −24.8369 | − | 24.8369i | −1.74751 | − | 1.74751i | ||||
\(203\) | 1.10685 | + | 0.296580i | 0.0776858 | + | 0.0208159i | ||||
\(204\) | 0.379054 | − | 0.656541i | 0.0265391 | − | 0.0459671i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −10.8541 | + | 18.7999i | −0.756241 | + | 1.30985i | ||||
\(207\) | 3.83838 | + | 14.3250i | 0.266786 | + | 0.995658i | ||||
\(208\) | 1.31105 | − | 1.31105i | 0.0909048 | − | 0.0909048i | ||||
\(209\) | −8.02850 | + | 0.927051i | −0.555343 | + | 0.0641255i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.8435 | − | 9.14723i | −1.09071 | − | 0.629721i | −0.156944 | − | 0.987608i | \(-0.550164\pi\) |
−0.933765 | + | 0.357887i | \(0.883497\pi\) | |||||||
\(212\) | −39.0393 | + | 10.4605i | −2.68123 | + | 0.718433i | ||||
\(213\) | 0.382883 | − | 1.42894i | 0.0262347 | − | 0.0979094i | ||||
\(214\) | 2.11111 | + | 1.21885i | 0.144312 | + | 0.0833187i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.00000 | −0.340207 | ||||||||
\(217\) | 1.81182 | + | 1.81182i | 0.122995 | + | 0.122995i | ||||
\(218\) | 8.72912 | − | 32.5775i | 0.591211 | − | 2.20643i | ||||
\(219\) | 2.26728 | + | 3.92705i | 0.153209 | + | 0.265366i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 1.22665i | − | 0.0825131i | ||||||
\(222\) | −2.14607 | + | 8.00926i | −0.144035 | + | 0.537546i | ||||
\(223\) | 4.36216 | + | 16.2798i | 0.292112 | + | 1.09018i | 0.943484 | + | 0.331418i | \(0.107527\pi\) |
−0.651372 | + | 0.758759i | \(0.725806\pi\) | |||||||
\(224\) | 5.80948 | + | 10.0623i | 0.388162 | + | 0.672316i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 13.7812 | − | 23.8697i | 0.916709 | − | 1.58779i | ||||
\(227\) | −9.52624 | − | 9.52624i | −0.632279 | − | 0.632279i | 0.316360 | − | 0.948639i | \(-0.397539\pi\) |
−0.948639 | + | 0.316360i | \(0.897539\pi\) | |||||||
\(228\) | −3.91372 | − | 3.10345i | −0.259192 | − | 0.205531i | ||||
\(229\) | − | 11.0000i | − | 0.726900i | −0.931614 | − | 0.363450i | \(-0.881599\pi\) | ||
0.931614 | − | 0.363450i | \(-0.118401\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.06231 | + | 0.613323i | 0.0698946 | + | 0.0403537i | ||||
\(232\) | 1.42894 | + | 0.382883i | 0.0938145 | + | 0.0251375i | ||||
\(233\) | 8.76011 | − | 2.34727i | 0.573894 | − | 0.153774i | 0.0398121 | − | 0.999207i | \(-0.487324\pi\) |
0.534082 | + | 0.845433i | \(0.320657\pi\) | |||||||
\(234\) | −10.2475 | + | 5.91641i | −0.669901 | + | 0.386768i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 42.7959i | 2.78577i | ||||||||
\(237\) | −5.01910 | − | 1.34486i | −0.326025 | − | 0.0873583i | ||||
\(238\) | 2.47500 | + | 0.663174i | 0.160430 | + | 0.0429872i | ||||
\(239\) | 23.8328i | 1.54162i | 0.637067 | + | 0.770808i | \(0.280147\pi\) | ||||
−0.637067 | + | 0.770808i | \(0.719853\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.2812 | + | 7.66788i | −0.855514 | + | 0.493931i | −0.862508 | − | 0.506044i | \(-0.831107\pi\) |
0.00699331 | + | 0.999976i | \(0.497774\pi\) | |||||||
\(242\) | −16.3336 | + | 4.37659i | −1.04997 | + | 0.281338i | ||||
\(243\) | −9.32358 | − | 2.49824i | −0.598108 | − | 0.160262i | ||||
\(244\) | 24.8436 | + | 14.3435i | 1.59045 | + | 0.918246i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | − | 3.87298i | − | 0.246932i | ||||||
\(247\) | −7.99487 | − | 1.18247i | −0.508701 | − | 0.0752385i | ||||
\(248\) | 2.33905 | + | 2.33905i | 0.148530 | + | 0.148530i | ||||
\(249\) | 2.85078 | − | 4.93769i | 0.180661 | − | 0.312914i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.13525 | + | 5.43042i | 0.197896 | + | 0.342765i | 0.947846 | − | 0.318729i | \(-0.103256\pi\) |
−0.749950 | + | 0.661494i | \(0.769923\pi\) | |||||||
\(252\) | −3.83838 | − | 14.3250i | −0.241795 | − | 0.902391i | ||||
\(253\) | 2.49351 | − | 9.30592i | 0.156766 | − | 0.585058i | ||||
\(254\) | − | 25.8541i | − | 1.62223i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.50000 | + | 7.79423i | 0.281250 | + | 0.487139i | ||||
\(257\) | −6.67711 | + | 24.9193i | −0.416507 | + | 1.55442i | 0.365292 | + | 0.930893i | \(0.380969\pi\) |
−0.781799 | + | 0.623531i | \(0.785697\pi\) | |||||||
\(258\) | 1.93950 | + | 1.93950i | 0.120748 | + | 0.120748i | ||||
\(259\) | −16.8151 | −1.04484 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.63525 | + | 0.944115i | 0.101220 | + | 0.0584392i | ||||
\(262\) | 10.5738 | − | 39.4620i | 0.653253 | − | 2.43797i | ||||
\(263\) | 12.5011 | − | 3.34967i | 0.770853 | − | 0.206549i | 0.148104 | − | 0.988972i | \(-0.452683\pi\) |
0.622748 | + | 0.782422i | \(0.286016\pi\) | |||||||
\(264\) | 1.37143 | + | 0.791796i | 0.0844057 | + | 0.0487317i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6.70820 | − | 15.4919i | 0.411306 | − | 0.949871i | ||||
\(267\) | 0.688681 | − | 0.688681i | 0.0421466 | − | 0.0421466i | ||||
\(268\) | −4.65874 | − | 17.3867i | −0.284578 | − | 1.06206i | ||||
\(269\) | 7.41517 | − | 12.8435i | 0.452111 | − | 0.783080i | −0.546406 | − | 0.837521i | \(-0.684004\pi\) |
0.998517 | + | 0.0544410i | \(0.0173377\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.281153 | + | 0.486971i | −0.0170788 | + | 0.0295814i | −0.874439 | − | 0.485136i | \(-0.838770\pi\) |
0.857360 | + | 0.514718i | \(0.172103\pi\) | |||||||
\(272\) | −0.639042 | − | 0.171231i | −0.0387476 | − | 0.0103824i | ||||
\(273\) | 0.867369 | + | 0.867369i | 0.0524956 | + | 0.0524956i | ||||
\(274\) | −8.66025 | −0.523185 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.15654 | − | 2.97713i | 0.310387 | − | 0.179202i | ||||
\(277\) | −19.5959 | + | 19.5959i | −1.17740 | + | 1.17740i | −0.197001 | + | 0.980403i | \(0.563120\pi\) |
−0.980403 | + | 0.197001i | \(0.936880\pi\) | |||||||
\(278\) | −3.85433 | + | 3.85433i | −0.231168 | + | 0.231168i | ||||
\(279\) | 2.11111 | + | 3.65654i | 0.126389 | + | 0.218911i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.50000 | + | 2.59808i | −0.268447 | + | 0.154988i | −0.628182 | − | 0.778067i | \(-0.716201\pi\) |
0.359734 | + | 0.933055i | \(0.382867\pi\) | |||||||
\(282\) | −0.856153 | − | 3.19521i | −0.0509832 | − | 0.190272i | ||||
\(283\) | 30.5672 | − | 8.19045i | 1.81703 | − | 0.486871i | 0.820615 | − | 0.571482i | \(-0.193631\pi\) |
0.996414 | + | 0.0846102i | \(0.0269645\pi\) | |||||||
\(284\) | 11.6190 | 0.689458 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.68692 | 0.454537 | ||||||||
\(287\) | 7.58648 | − | 2.03279i | 0.447816 | − | 0.119992i | ||||
\(288\) | 4.95532 | + | 18.4935i | 0.291995 | + | 1.08974i | ||||
\(289\) | 14.3434 | − | 8.28115i | 0.843728 | − | 0.487127i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.63525 | − | 2.83234i | −0.0958603 | − | 0.166035i | ||||
\(292\) | −25.1836 | + | 25.1836i | −1.47376 | + | 1.47376i | ||||
\(293\) | 4.01196 | − | 4.01196i | 0.234381 | − | 0.234381i | −0.580138 | − | 0.814519i | \(-0.697001\pi\) |
0.814519 | + | 0.580138i | \(0.197001\pi\) | |||||||
\(294\) | 2.95870 | − | 1.70820i | 0.172555 | − | 0.0996245i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −21.7082 | −1.26176 | ||||||||
\(297\) | 2.93159 | + | 2.93159i | 0.170108 | + | 0.170108i | ||||
\(298\) | −20.9685 | − | 5.61850i | −1.21467 | − | 0.325471i | ||||
\(299\) | 4.81710 | − | 8.34346i | 0.278580 | − | 0.482515i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.78115 | + | 4.81710i | −0.160303 | + | 0.277653i | ||||
\(302\) | −2.71471 | − | 10.1314i | −0.156214 | − | 0.582998i | ||||
\(303\) | −4.24264 | + | 4.24264i | −0.243733 | + | 0.243733i | ||||
\(304\) | −1.73205 | + | 4.00000i | −0.0993399 | + | 0.229416i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.65654 | + | 2.11111i | 0.209031 | + | 0.120684i | ||||
\(307\) | 18.0707 | − | 4.84204i | 1.03135 | − | 0.276350i | 0.296826 | − | 0.954931i | \(-0.404072\pi\) |
0.734525 | + | 0.678582i | \(0.237405\pi\) | |||||||
\(308\) | −2.49351 | + | 9.30592i | −0.142081 | + | 0.530254i | ||||
\(309\) | 3.21140 | + | 1.85410i | 0.182690 | + | 0.105476i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.00000 | −0.510343 | −0.255172 | − | 0.966896i | \(-0.582132\pi\) | ||||
−0.255172 | + | 0.966896i | \(0.582132\pi\) | |||||||
\(312\) | 1.11977 | + | 1.11977i | 0.0633944 | + | 0.0633944i | ||||
\(313\) | 3.00721 | − | 11.2230i | 0.169977 | − | 0.634364i | −0.827375 | − | 0.561649i | \(-0.810167\pi\) |
0.997353 | − | 0.0727147i | \(-0.0231663\pi\) | |||||||
\(314\) | 1.65396 | + | 2.86475i | 0.0933384 | + | 0.161667i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 40.8111i | − | 2.29580i | ||||||
\(317\) | 4.62990 | − | 17.2790i | 0.260041 | − | 0.970486i | −0.705175 | − | 0.709033i | \(-0.749132\pi\) |
0.965216 | − | 0.261453i | \(-0.0842016\pi\) | |||||||
\(318\) | 2.97812 | + | 11.1145i | 0.167005 | + | 0.623270i | ||||
\(319\) | −0.613323 | − | 1.06231i | −0.0343395 | − | 0.0594777i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.208204 | − | 0.360620i | 0.0116208 | − | 0.0201278i | ||||
\(322\) | 14.2302 | + | 14.2302i | 0.793021 | + | 0.793021i | ||||
\(323\) | 1.06097 | + | 2.68152i | 0.0590340 | + | 0.149204i | ||||
\(324\) | − | 23.1246i | − | 1.28470i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.35410 | − | 1.93649i | −0.185767 | − | 0.107252i | ||||
\(327\) | −5.56490 | − | 1.49111i | −0.307740 | − | 0.0824587i | ||||
\(328\) | 9.79410 | − | 2.62432i | 0.540789 | − | 0.144904i | ||||
\(329\) | 5.80948 | − | 3.35410i | 0.320287 | − | 0.184918i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.3923i | 0.571213i | 0.958347 | + | 0.285606i | \(0.0921950\pi\) | ||||
−0.958347 | + | 0.285606i | \(0.907805\pi\) | |||||||
\(332\) | 43.2548 | + | 11.5901i | 2.37391 | + | 0.636088i | ||||
\(333\) | −26.7641 | − | 7.17141i | −1.46666 | − | 0.392991i | ||||
\(334\) | − | 12.5623i | − | 0.687379i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.572949 | − | 0.330792i | 0.0312569 | − | 0.0180462i | ||||
\(337\) | 19.4389 | − | 5.20863i | 1.05890 | − | 0.283732i | 0.312977 | − | 0.949761i | \(-0.398674\pi\) |
0.745926 | + | 0.666028i | \(0.232007\pi\) | |||||||
\(338\) | −20.6534 | − | 5.53406i | −1.12340 | − | 0.301013i | ||||
\(339\) | −4.07742 | − | 2.35410i | −0.221455 | − | 0.127857i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 2.74286i | − | 0.148534i | ||||||
\(342\) | 17.2843 | − | 21.7971i | 0.934630 | − | 1.17865i | ||||
\(343\) | 13.4722 | + | 13.4722i | 0.727430 | + | 0.727430i | ||||
\(344\) | −3.59045 | + | 6.21885i | −0.193584 | + | 0.335298i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.06231 | − | 8.76817i | −0.272151 | − | 0.471380i | ||||
\(347\) | 5.84318 | + | 21.8070i | 0.313678 | + | 1.17066i | 0.925214 | + | 0.379446i | \(0.123886\pi\) |
−0.611535 | + | 0.791217i | \(0.709448\pi\) | |||||||
\(348\) | 0.196213 | − | 0.732277i | 0.0105181 | − | 0.0392541i | ||||
\(349\) | − | 11.0000i | − | 0.588817i | −0.955680 | − | 0.294408i | \(-0.904877\pi\) | ||
0.955680 | − | 0.294408i | \(-0.0951225\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.07295 | + | 3.59045i | 0.110646 | + | 0.191644i | ||||
\(352\) | 3.21911 | − | 12.0139i | 0.171579 | − | 0.640342i | ||||
\(353\) | −15.5643 | − | 15.5643i | −0.828405 | − | 0.828405i | 0.158892 | − | 0.987296i | \(-0.449208\pi\) |
−0.987296 | + | 0.158892i | \(0.949208\pi\) | |||||||
\(354\) | 12.1840 | 0.647573 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.62461 | + | 3.82472i | 0.351104 | + | 0.202710i | ||||
\(357\) | 0.113284 | − | 0.422780i | 0.00599560 | − | 0.0223759i | ||||
\(358\) | 19.5882 | − | 5.24864i | 1.03527 | − | 0.277399i | ||||
\(359\) | 26.8284 | + | 15.4894i | 1.41595 | + | 0.817497i | 0.995940 | − | 0.0900240i | \(-0.0286944\pi\) |
0.420007 | + | 0.907521i | \(0.362028\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.5000 | − | 4.33013i | 0.973684 | − | 0.227901i | ||||
\(362\) | 24.2480 | − | 24.2480i | 1.27444 | − | 1.27444i | ||||
\(363\) | 0.747610 | + | 2.79012i | 0.0392394 | + | 0.146443i | ||||
\(364\) | −4.81710 | + | 8.34346i | −0.252485 | + | 0.437316i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4.08359 | − | 7.07299i | 0.213453 | − | 0.369711i | ||||
\(367\) | 18.1593 | + | 4.86576i | 0.947906 | + | 0.253991i | 0.699473 | − | 0.714659i | \(-0.253418\pi\) |
0.248433 | + | 0.968649i | \(0.420085\pi\) | |||||||
\(368\) | −3.67423 | − | 3.67423i | −0.191533 | − | 0.191533i | ||||
\(369\) | 12.9421 | 0.673740 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −20.2082 | + | 11.6672i | −1.04916 | + | 0.605731i | ||||
\(372\) | 1.19867 | − | 1.19867i | 0.0621484 | − | 0.0621484i | ||||
\(373\) | −10.7979 | + | 10.7979i | −0.559093 | + | 0.559093i | −0.929049 | − | 0.369956i | \(-0.879373\pi\) |
0.369956 | + | 0.929049i | \(0.379373\pi\) | |||||||
\(374\) | −1.37143 | − | 2.37539i | −0.0709150 | − | 0.122828i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.50000 | − | 4.33013i | 0.386783 | − | 0.223309i | ||||
\(377\) | −0.317479 | − | 1.18485i | −0.0163510 | − | 0.0610228i | ||||
\(378\) | −8.36516 | + | 2.24144i | −0.430258 | + | 0.115287i | ||||
\(379\) | −27.2074 | −1.39755 | −0.698775 | − | 0.715341i | \(-0.746271\pi\) | ||||
−0.698775 | + | 0.715341i | \(0.746271\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.41641 | −0.226259 | ||||||||
\(382\) | 15.4343 | − | 4.13560i | 0.789685 | − | 0.211595i | ||||
\(383\) | 4.64432 | + | 17.3328i | 0.237314 | + | 0.885667i | 0.977092 | + | 0.212816i | \(0.0682635\pi\) |
−0.739779 | + | 0.672850i | \(0.765070\pi\) | |||||||
\(384\) | 5.17772 | − | 2.98936i | 0.264224 | − | 0.152550i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.27051 | − | 16.0570i | −0.471857 | − | 0.817279i | ||||
\(387\) | −6.48110 | + | 6.48110i | −0.329453 | + | 0.329453i | ||||
\(388\) | 18.1634 | − | 18.1634i | 0.922107 | − | 0.922107i | ||||
\(389\) | 1.60570 | − | 0.927051i | 0.0814122 | − | 0.0470034i | −0.458741 | − | 0.888570i | \(-0.651700\pi\) |
0.540153 | + | 0.841567i | \(0.318366\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.43769 | −0.173852 | ||||||||
\(392\) | 6.32456 | + | 6.32456i | 0.319438 | + | 0.319438i | ||||
\(393\) | −6.74092 | − | 1.80622i | −0.340034 | − | 0.0911119i | ||||
\(394\) | −2.11111 | + | 3.65654i | −0.106356 | + | 0.184214i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −7.93769 | + | 13.7485i | −0.398884 | + | 0.690888i | ||||
\(397\) | −5.69693 | − | 21.2612i | −0.285921 | − | 1.06707i | −0.948164 | − | 0.317782i | \(-0.897062\pi\) |
0.662243 | − | 0.749289i | \(-0.269605\pi\) | |||||||
\(398\) | −33.4009 | + | 33.4009i | −1.67424 | + | 1.67424i | ||||
\(399\) | −2.64634 | − | 1.14590i | −0.132483 | − | 0.0573667i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.5623 | + | 13.6037i | 1.17665 | + | 0.679337i | 0.955236 | − | 0.295844i | \(-0.0956010\pi\) |
0.221409 | + | 0.975181i | \(0.428934\pi\) | |||||||
\(402\) | −4.94999 | + | 1.32635i | −0.246883 | + | 0.0661522i | ||||
\(403\) | 0.709905 | − | 2.64940i | 0.0353629 | − | 0.131976i | ||||
\(404\) | −40.8111 | − | 23.5623i | −2.03043 | − | 1.17227i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.56231 | 0.127165 | ||||||||
\(407\) | 12.7279 | + | 12.7279i | 0.630900 | + | 0.630900i | ||||
\(408\) | 0.146248 | − | 0.545807i | 0.00724038 | − | 0.0270215i | ||||
\(409\) | −11.6190 | − | 20.1246i | −0.574520 | − | 0.995098i | −0.996094 | − | 0.0883038i | \(-0.971855\pi\) |
0.421573 | − | 0.906794i | \(-0.361478\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.47935i | 0.0729709i | ||||||||
\(412\) | −7.53800 | + | 28.1322i | −0.371371 | + | 1.38597i | ||||
\(413\) | 6.39495 | + | 23.8663i | 0.314675 | + | 1.17438i | ||||
\(414\) | 16.5808 | + | 28.7188i | 0.814904 | + | 1.41145i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 6.21885 | − | 10.7714i | 0.304904 | − | 0.528109i | ||||
\(417\) | 0.658399 | + | 0.658399i | 0.0322419 | + | 0.0322419i | ||||
\(418\) | −16.8040 | + | 6.64870i | −0.821912 | + | 0.325199i | ||||
\(419\) | 31.4164i | 1.53479i | 0.641173 | + | 0.767396i | \(0.278448\pi\) | ||||
−0.641173 | + | 0.767396i | \(0.721552\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.1246 | − | 16.8151i | −1.41945 | − | 0.819518i | −0.423197 | − | 0.906038i | \(-0.639092\pi\) |
−0.996250 | + | 0.0865199i | \(0.972425\pi\) | |||||||
\(422\) | −39.5137 | − | 10.5877i | −1.92350 | − | 0.515400i | ||||
\(423\) | 10.6772 | − | 2.86096i | 0.519145 | − | 0.139104i | ||||
\(424\) | −26.0887 | + | 15.0623i | −1.26698 | + | 0.731490i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 3.30792i | − | 0.160269i | ||||||
\(427\) | 15.9980 | + | 4.28666i | 0.774200 | + | 0.207446i | ||||
\(428\) | 3.15907 | + | 0.846470i | 0.152699 | + | 0.0409157i | ||||
\(429\) | − | 1.31308i | − | 0.0633962i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.9271 | + | 12.6596i | −1.05619 | + | 0.609791i | −0.924376 | − | 0.381484i | \(-0.875413\pi\) |
−0.131813 | + | 0.991275i | \(0.542080\pi\) | |||||||
\(432\) | 2.15988 | − | 0.578737i | 0.103917 | − | 0.0278445i | ||||
\(433\) | 13.6433 | + | 3.65572i | 0.655656 | + | 0.175683i | 0.571285 | − | 0.820752i | \(-0.306445\pi\) |
0.0843715 | + | 0.996434i | \(0.473112\pi\) | |||||||
\(434\) | 4.96188 | + | 2.86475i | 0.238178 | + | 0.137512i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 45.2492i | − | 2.16704i | ||||||
\(437\) | −3.31388 | + | 22.4058i | −0.158524 | + | 1.07181i | ||||
\(438\) | 7.16978 | + | 7.16978i | 0.342585 | + | 0.342585i | ||||
\(439\) | 12.7377 | − | 22.0623i | 0.607936 | − | 1.05298i | −0.383644 | − | 0.923481i | \(-0.625331\pi\) |
0.991580 | − | 0.129495i | \(-0.0413357\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.70820 | + | 9.88690i | 0.271819 | + | 0.470805i | ||||
\(442\) | −0.709905 | − | 2.64940i | −0.0337667 | − | 0.126019i | ||||
\(443\) | −8.41164 | + | 31.3927i | −0.399649 | + | 1.49151i | 0.414066 | + | 0.910247i | \(0.364108\pi\) |
−0.813715 | + | 0.581264i | \(0.802558\pi\) | |||||||
\(444\) | 11.1246i | 0.527951i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 18.8435 | + | 32.6378i | 0.892264 | + | 1.54545i | ||||
\(447\) | −0.959754 | + | 3.58185i | −0.0453948 | + | 0.169416i | ||||
\(448\) | 15.9217 | + | 15.9217i | 0.752229 | + | 0.752229i | ||||
\(449\) | −14.2653 | −0.673221 | −0.336610 | − | 0.941644i | \(-0.609280\pi\) | ||||
−0.336610 | + | 0.941644i | \(0.609280\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.28115 | − | 4.20378i | −0.342856 | − | 0.197948i | ||||
\(452\) | 9.57080 | − | 35.7187i | 0.450172 | − | 1.68007i | ||||
\(453\) | −1.73065 | + | 0.463728i | −0.0813133 | + | 0.0217878i | ||||
\(454\) | −26.0887 | − | 15.0623i | −1.22440 | − | 0.706909i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.41641 | − | 1.47935i | −0.159988 | − | 0.0692768i | ||||
\(457\) | −24.1375 | + | 24.1375i | −1.12911 | + | 1.12911i | −0.138783 | + | 0.990323i | \(0.544319\pi\) |
−0.990323 | + | 0.138783i | \(0.955681\pi\) | |||||||
\(458\) | −6.36611 | − | 23.7586i | −0.297469 | − | 1.11017i | ||||
\(459\) | 0.739674 | − | 1.28115i | 0.0345250 | − | 0.0597991i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.71885 | + | 2.97713i | −0.0800547 | + | 0.138659i | −0.903273 | − | 0.429066i | \(-0.858843\pi\) |
0.823219 | + | 0.567725i | \(0.192176\pi\) | |||||||
\(462\) | 2.64940 | + | 0.709905i | 0.123261 | + | 0.0330278i | ||||
\(463\) | −17.8351 | − | 17.8351i | −0.828868 | − | 0.828868i | 0.158492 | − | 0.987360i | \(-0.449337\pi\) |
−0.987360 | + | 0.158492i | \(0.949337\pi\) | |||||||
\(464\) | −0.661585 | −0.0307133 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 17.5623 | − | 10.1396i | 0.813558 | − | 0.469708i | ||||
\(467\) | −3.60598 | + | 3.60598i | −0.166865 | + | 0.166865i | −0.785600 | − | 0.618735i | \(-0.787646\pi\) |
0.618735 | + | 0.785600i | \(0.287646\pi\) | |||||||
\(468\) | −11.2256 | + | 11.2256i | −0.518903 | + | 0.518903i | ||||
\(469\) | −5.19615 | − | 9.00000i | −0.239936 | − | 0.415581i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.489357 | − | 0.282530i | 0.0225484 | − | 0.0130183i | ||||
\(472\) | 8.25585 | + | 30.8113i | 0.380006 | + | 1.41820i | ||||
\(473\) | 5.75137 | − | 1.54108i | 0.264448 | − | 0.0708588i | ||||
\(474\) | −11.6190 | −0.533676 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.43769 | 0.157566 | ||||||||
\(477\) | −37.1407 | + | 9.95181i | −1.70055 | + | 0.455662i | ||||
\(478\) | 13.7929 | + | 51.4759i | 0.630874 | + | 2.35445i | ||||
\(479\) | −22.6246 | + | 13.0623i | −1.03374 | + | 0.596832i | −0.918055 | − | 0.396454i | \(-0.870241\pi\) |
−0.115689 | + | 0.993286i | \(0.536907\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.00000 | + | 15.5885i | 0.410365 | + | 0.710772i | ||||
\(482\) | −24.2480 | + | 24.2480i | −1.10446 | + | 1.10446i | ||||
\(483\) | 2.43082 | − | 2.43082i | 0.110606 | − | 0.110606i | ||||
\(484\) | −19.6474 | + | 11.3435i | −0.893066 | + | 0.515612i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −21.5836 | −0.979052 | ||||||||
\(487\) | −18.4729 | − | 18.4729i | −0.837087 | − | 0.837087i | 0.151388 | − | 0.988474i | \(-0.451626\pi\) |
−0.988474 | + | 0.151388i | \(0.951626\pi\) | |||||||
\(488\) | 20.6534 | + | 5.53406i | 0.934935 | + | 0.250515i | ||||
\(489\) | −0.330792 | + | 0.572949i | −0.0149589 | + | 0.0259097i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.06231 | + | 7.03612i | −0.183329 | + | 0.317536i | −0.943012 | − | 0.332758i | \(-0.892021\pi\) |
0.759683 | + | 0.650294i | \(0.225354\pi\) | |||||||
\(492\) | −1.34486 | − | 5.01910i | −0.0606311 | − | 0.226278i | ||||
\(493\) | −0.309496 | + | 0.309496i | −0.0139390 | + | 0.0139390i | ||||
\(494\) | −17.9523 | + | 2.07295i | −0.807711 | + | 0.0932664i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.28115 | − | 0.739674i | −0.0575255 | − | 0.0332123i | ||||
\(497\) | 6.47963 | − | 1.73621i | 0.290651 | − | 0.0778797i | ||||
\(498\) | 3.29970 | − | 12.3147i | 0.147863 | − | 0.551833i | ||||
\(499\) | 26.0887 | + | 15.0623i | 1.16789 | + | 0.674281i | 0.953182 | − | 0.302397i | \(-0.0977868\pi\) |
0.214708 | + | 0.976678i | \(0.431120\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.14590 | −0.0958717 | ||||||||
\(502\) | 9.91455 | + | 9.91455i | 0.442508 | + | 0.442508i | ||||
\(503\) | −7.70174 | + | 28.7433i | −0.343403 | + | 1.28160i | 0.551063 | + | 0.834464i | \(0.314222\pi\) |
−0.894466 | + | 0.447135i | \(0.852444\pi\) | |||||||
\(504\) | −5.52694 | − | 9.57295i | −0.246190 | − | 0.426413i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 21.5427i | − | 0.957691i | ||||||
\(507\) | −0.945330 | + | 3.52802i | −0.0419836 | + | 0.156685i | ||||
\(508\) | −8.97763 | − | 33.5050i | −0.398318 | − | 1.48654i | ||||
\(509\) | 16.1535 | + | 27.9787i | 0.715992 | + | 1.24013i | 0.962576 | + | 0.271013i | \(0.0873587\pi\) |
−0.246584 | + | 0.969122i | \(0.579308\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.2812 | + | 17.8075i | −0.454811 | + | 0.787757i | ||||
\(512\) | −7.90569 | − | 7.90569i | −0.349386 | − | 0.349386i | ||||
\(513\) | −7.63710 | − | 6.05596i | −0.337186 | − | 0.267377i | ||||
\(514\) | 57.6869i | 2.54446i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.18692 | + | 1.83997i | 0.140296 | + | 0.0810001i | ||||
\(517\) | −6.93622 | − | 1.85856i | −0.305055 | − | 0.0817392i | ||||
\(518\) | −36.3185 | + | 9.73152i | −1.59574 | + | 0.427579i | ||||
\(519\) | −1.49778 | + | 0.864745i | −0.0657454 | + | 0.0379581i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.5306i | 1.24995i | 0.780646 | + | 0.624974i | \(0.214890\pi\) | ||||
−0.780646 | + | 0.624974i | \(0.785110\pi\) | |||||||
\(522\) | 4.07834 | + | 1.09279i | 0.178504 | + | 0.0478300i | ||||
\(523\) | −1.52963 | − | 0.409864i | −0.0668862 | − | 0.0179221i | 0.225221 | − | 0.974308i | \(-0.427690\pi\) |
−0.292107 | + | 0.956386i | \(0.594356\pi\) | |||||||
\(524\) | − | 54.8115i | − | 2.39445i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 25.0623 | − | 14.4697i | 1.09277 | − | 0.630910i | ||||
\(527\) | −0.945365 | + | 0.253310i | −0.0411807 | + | 0.0110343i | ||||
\(528\) | −0.684072 | − | 0.183297i | −0.0297704 | − | 0.00797696i | ||||
\(529\) | −3.46410 | − | 2.00000i | −0.150613 | − | 0.0869565i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 40.7146i | 1.76686i | ||||||||
\(532\) | 3.31388 | − | 22.4058i | 0.143675 | − | 0.971413i | ||||
\(533\) | −5.94504 | − | 5.94504i | −0.257508 | − | 0.257508i | ||||
\(534\) | 1.08890 | − | 1.88603i | 0.0471213 | − | 0.0816166i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.70820 | − | 11.6190i | −0.289750 | − | 0.501862i | ||||
\(537\) | −0.896575 | − | 3.34607i | −0.0386901 | − | 0.144393i | ||||
\(538\) | 8.58287 | − | 32.0317i | 0.370034 | − | 1.38099i | ||||
\(539\) | − | 7.41641i | − | 0.319447i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.2812 | − | 21.2716i | −0.528008 | − | 0.914537i | −0.999467 | − | 0.0326487i | \(-0.989606\pi\) |
0.471459 | − | 0.881888i | \(-0.343728\pi\) | |||||||
\(542\) | −0.325427 | + | 1.21451i | −0.0139783 | + | 0.0521677i | ||||
\(543\) | −4.14205 | − | 4.14205i | −0.177752 | − | 0.177752i | ||||
\(544\) | −4.43804 | −0.190280 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.37539 | + | 1.37143i | 0.101657 | + | 0.0586918i | ||||
\(547\) | 0.366593 | − | 1.36814i | 0.0156744 | − | 0.0584977i | −0.957646 | − | 0.287949i | \(-0.907027\pi\) |
0.973320 | + | 0.229452i | \(0.0736932\pi\) | |||||||
\(548\) | −11.2230 | + | 3.00721i | −0.479425 | + | 0.128461i | ||||
\(549\) | 23.6354 | + | 13.6459i | 1.00873 | + | 0.582393i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.71885 | + | 2.31555i | 0.0732253 | + | 0.0986456i | ||||
\(552\) | 3.13817 | − | 3.13817i | 0.133569 | − | 0.133569i | ||||
\(553\) | −6.09837 | − | 22.7594i | −0.259329 | − | 0.967830i | ||||
\(554\) | −30.9839 | + | 53.6656i | −1.31638 | + | 2.28003i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.65654 | + | 6.33332i | −0.155072 | + | 0.268592i | ||||
\(557\) | 4.28682 | + | 1.14865i | 0.181638 | + | 0.0486699i | 0.348492 | − | 0.937312i | \(-0.386694\pi\) |
−0.166853 | + | 0.985982i | \(0.553361\pi\) | |||||||
\(558\) | 6.67590 | + | 6.67590i | 0.282613 | + | 0.282613i | ||||
\(559\) | 5.95426 | 0.251838 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.405765 | + | 0.234268i | −0.0171314 | + | 0.00989082i | ||||
\(562\) | −8.21584 | + | 8.21584i | −0.346564 | + | 0.346564i | ||||
\(563\) | −16.7005 | + | 16.7005i | −0.703841 | + | 0.703841i | −0.965233 | − | 0.261392i | \(-0.915819\pi\) |
0.261392 | + | 0.965233i | \(0.415819\pi\) | |||||||
\(564\) | −2.21902 | − | 3.84346i | −0.0934377 | − | 0.161839i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 61.2812 | − | 35.3807i | 2.57584 | − | 1.48716i | ||||
\(567\) | −3.45549 | − | 12.8961i | −0.145117 | − | 0.541584i | ||||
\(568\) | 8.36516 | − | 2.24144i | 0.350994 | − | 0.0940487i | ||||
\(569\) | −40.2461 | −1.68720 | −0.843601 | − | 0.536970i | \(-0.819569\pi\) | ||||
−0.843601 | + | 0.536970i | \(0.819569\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.1246 | 0.884037 | 0.442019 | − | 0.897006i | \(-0.354262\pi\) | ||||
0.442019 | + | 0.897006i | \(0.354262\pi\) | |||||||
\(572\) | 9.96167 | − | 2.66922i | 0.416518 | − | 0.111606i | ||||
\(573\) | −0.706444 | − | 2.63649i | −0.0295121 | − | 0.110141i | ||||
\(574\) | 15.2094 | − | 8.78115i | 0.634828 | − | 0.366518i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 18.5517 | + | 32.1324i | 0.772986 | + | 1.33885i | ||||
\(577\) | 16.4317 | − | 16.4317i | 0.684060 | − | 0.684060i | −0.276853 | − | 0.960912i | \(-0.589291\pi\) |
0.960912 | + | 0.276853i | \(0.0892914\pi\) | |||||||
\(578\) | 26.1873 | − | 26.1873i | 1.08925 | − | 1.08925i | ||||
\(579\) | −2.74286 | + | 1.58359i | −0.113989 | + | 0.0658118i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 25.8541 | 1.07261 | ||||||||
\(582\) | −5.17113 | − | 5.17113i | −0.214350 | − | 0.214350i | ||||
\(583\) | 24.1276 | + | 6.46497i | 0.999262 | + | 0.267752i | ||||
\(584\) | −13.2729 | + | 22.9894i | −0.549237 | + | 0.951306i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.34346 | − | 10.9872i | 0.262046 | − | 0.453877i | ||||
\(587\) | −5.03699 | − | 18.7983i | −0.207899 | − | 0.775889i | −0.988546 | − | 0.150918i | \(-0.951777\pi\) |
0.780647 | − | 0.624972i | \(-0.214889\pi\) | |||||||
\(588\) | 3.24109 | − | 3.24109i | 0.133660 | − | 0.133660i | ||||
\(589\) | 0.739674 | + | 6.40576i | 0.0304777 | + | 0.263945i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.624612 | + | 0.360620i | 0.0256931 | + | 0.0148339i | ||||
\(592\) | 9.37740 | − | 2.51267i | 0.385409 | − | 0.103270i | ||||
\(593\) | 3.34967 | − | 12.5011i | 0.137554 | − | 0.513360i | −0.862420 | − | 0.506193i | \(-0.831052\pi\) |
0.999974 | − | 0.00716635i | \(-0.00228114\pi\) | |||||||
\(594\) | 8.02850 | + | 4.63525i | 0.329413 | + | 0.190187i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −29.1246 | −1.19299 | ||||||||
\(597\) | 5.70556 | + | 5.70556i | 0.233513 | + | 0.233513i | ||||
\(598\) | 5.57567 | − | 20.8087i | 0.228006 | − | 0.850930i | ||||
\(599\) | −2.97713 | − | 5.15654i | −0.121642 | − | 0.210691i | 0.798773 | − | 0.601632i | \(-0.205483\pi\) |
−0.920415 | + | 0.390942i | \(0.872149\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.1769i | 1.27173i | 0.771799 | + | 0.635866i | \(0.219357\pi\) | ||||
−0.771799 | + | 0.635866i | \(0.780643\pi\) | |||||||
\(602\) | −3.21911 | + | 12.0139i | −0.131201 | + | 0.489650i | ||||
\(603\) | −4.43218 | − | 16.5411i | −0.180492 | − | 0.673606i | ||||
\(604\) | −7.03612 | − | 12.1869i | −0.286296 | − | 0.495879i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.70820 | + | 11.6190i | −0.272502 | + | 0.471988i | ||||
\(607\) | 1.93004 | + | 1.93004i | 0.0783379 | + | 0.0783379i | 0.745190 | − | 0.666852i | \(-0.232359\pi\) |
−0.666852 | + | 0.745190i | \(0.732359\pi\) | |||||||
\(608\) | −4.27820 | + | 28.9257i | −0.173504 | + | 1.17309i | ||||
\(609\) | − | 0.437694i | − | 0.0177363i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.21885 | − | 3.59045i | −0.251588 | − | 0.145254i | ||||
\(612\) | 5.47167 | + | 1.46613i | 0.221179 | + | 0.0592648i | ||||
\(613\) | −17.9152 | + | 4.80036i | −0.723587 | + | 0.193885i | −0.601772 | − | 0.798668i | \(-0.705538\pi\) |
−0.121815 | + | 0.992553i | \(0.538872\pi\) | |||||||
\(614\) | 36.2283 | − | 20.9164i | 1.46205 | − | 0.844118i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.18091i | 0.289327i | ||||||||
\(617\) | 27.6517 | + | 7.40924i | 1.11321 | + | 0.298285i | 0.768134 | − | 0.640289i | \(-0.221185\pi\) |
0.345079 | + | 0.938573i | \(0.387852\pi\) | |||||||
\(618\) | 8.00926 | + | 2.14607i | 0.322180 | + | 0.0863278i | ||||
\(619\) | − | 12.5623i | − | 0.504922i | −0.967607 | − | 0.252461i | \(-0.918760\pi\) | ||
0.967607 | − | 0.252461i | \(-0.0812399\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.0623 | − | 5.80948i | 0.403786 | − | 0.233126i | ||||
\(622\) | −19.4389 | + | 5.20863i | −0.779428 | + | 0.208847i | ||||
\(623\) | 4.26592 | + | 1.14305i | 0.170911 | + | 0.0457953i | ||||
\(624\) | −0.613323 | − | 0.354102i | −0.0245526 | − | 0.0141754i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 25.9808i | − | 1.03840i | ||||||
\(627\) | 1.13573 | + | 2.87047i | 0.0453569 | + | 0.114636i | ||||
\(628\) | 3.13817 | + | 3.13817i | 0.125227 | + | 0.125227i | ||||
\(629\) | 3.21140 | − | 5.56231i | 0.128047 | − | 0.221784i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.78115 | − | 11.7453i | −0.269953 | − | 0.467573i | 0.698896 | − | 0.715223i | \(-0.253675\pi\) |
−0.968850 | + | 0.247650i | \(0.920342\pi\) | |||||||
\(632\) | −7.87297 | − | 29.3823i | −0.313170 | − | 1.16877i | ||||
\(633\) | −1.80859 | + | 6.74975i | −0.0718850 | + | 0.268279i | ||||
\(634\) | − | 40.0000i | − | 1.58860i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 7.71885 | + | 13.3694i | 0.306072 | + | 0.530133i | ||||
\(637\) | 1.91951 | − | 7.16370i | 0.0760537 | − | 0.283836i | ||||
\(638\) | −1.93950 | − | 1.93950i | −0.0767854 | − | 0.0767854i | ||||
\(639\) | 11.0539 | 0.437285 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31.9058 | − | 18.4208i | −1.26020 | − | 0.727578i | −0.287088 | − | 0.957904i | \(-0.592687\pi\) |
−0.973113 | + | 0.230326i | \(0.926021\pi\) | |||||||
\(642\) | 0.240991 | − | 0.899389i | 0.00951114 | − | 0.0354961i | ||||
\(643\) | 29.6264 | − | 7.93837i | 1.16835 | − | 0.313059i | 0.378055 | − | 0.925783i | \(-0.376593\pi\) |
0.790297 | + | 0.612724i | \(0.209926\pi\) | |||||||
\(644\) | 23.3827 | + | 13.5000i | 0.921407 | + | 0.531975i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.84346 | + | 5.17772i | 0.151219 | + | 0.203715i | ||||
\(647\) | 22.5132 | − | 22.5132i | 0.885086 | − | 0.885086i | −0.108960 | − | 0.994046i | \(-0.534752\pi\) |
0.994046 | + | 0.108960i | \(0.0347521\pi\) | |||||||
\(648\) | −4.46102 | − | 16.6488i | −0.175246 | − | 0.654025i | ||||
\(649\) | 13.2246 | − | 22.9058i | 0.519113 | − | 0.899130i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.489357 | − | 0.847591i | 0.0191794 | − | 0.0332197i | ||||
\(652\) | −5.01910 | − | 1.34486i | −0.196563 | − | 0.0526689i | ||||
\(653\) | 6.48110 | + | 6.48110i | 0.253625 | + | 0.253625i | 0.822455 | − | 0.568830i | \(-0.192604\pi\) |
−0.568830 | + | 0.822455i | \(0.692604\pi\) | |||||||
\(654\) | −12.8825 | −0.503744 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.92705 | + | 2.26728i | −0.153326 | + | 0.0885226i | ||||
\(657\) | −23.9588 | + | 23.9588i | −0.934723 | + | 0.934723i | ||||
\(658\) | 10.6066 | − | 10.6066i | 0.413488 | − | 0.413488i | ||||
\(659\) | 4.58283 | + | 7.93769i | 0.178522 | + | 0.309209i | 0.941374 | − | 0.337364i | \(-0.109535\pi\) |
−0.762853 | + | 0.646572i | \(0.776202\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.21885 | − | 5.32250i | 0.358572 | − | 0.207021i | −0.309882 | − | 0.950775i | \(-0.600290\pi\) |
0.668454 | + | 0.743753i | \(0.266956\pi\) | |||||||
\(662\) | 6.01441 | + | 22.4461i | 0.233757 | + | 0.872392i | ||||
\(663\) | −0.452572 | + | 0.121266i | −0.0175764 | + | 0.00470959i | ||||
\(664\) | 33.3775 | 1.29530 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −61.9574 | −2.40080 | ||||||||
\(667\) | −3.32056 | + | 0.889741i | −0.128573 | + | 0.0344509i | ||||
\(668\) | −4.36216 | − | 16.2798i | −0.168777 | − | 0.629885i | ||||
\(669\) | 5.57521 | − | 3.21885i | 0.215550 | − | 0.124448i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.86475 | − | 15.3542i | −0.342220 | − | 0.592742i | ||||
\(672\) | 3.13817 | − | 3.13817i | 0.121058 | − | 0.121058i | ||||
\(673\) | 8.67656 | − | 8.67656i | 0.334457 | − | 0.334457i | −0.519819 | − | 0.854276i | \(-0.674001\pi\) |
0.854276 | + | 0.519819i | \(0.174001\pi\) | |||||||
\(674\) | 38.9711 | − | 22.5000i | 1.50111 | − | 0.866668i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −28.6869 | −1.10334 | ||||||||
\(677\) | 1.58114 | + | 1.58114i | 0.0607681 | + | 0.0607681i | 0.736838 | − | 0.676070i | \(-0.236318\pi\) |
−0.676070 | + | 0.736838i | \(0.736318\pi\) | |||||||
\(678\) | −10.1691 | − | 2.72481i | −0.390543 | − | 0.104646i | ||||
\(679\) | 7.41517 | − | 12.8435i | 0.284568 | − | 0.492887i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.57295 | + | 4.45648i | −0.0985956 | + | 0.170773i | ||||
\(682\) | −1.58740 | − | 5.92424i | −0.0607845 | − | 0.226851i | ||||
\(683\) | −15.9296 | + | 15.9296i | −0.609529 | + | 0.609529i | −0.942823 | − | 0.333294i | \(-0.891840\pi\) |
0.333294 | + | 0.942823i | \(0.391840\pi\) | |||||||
\(684\) | 14.8303 | − | 34.2492i | 0.567053 | − | 1.30955i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 36.8951 | + | 21.3014i | 1.40866 | + | 0.813292i | ||||
\(687\) | −4.05846 | + | 1.08746i | −0.154840 | + | 0.0414892i | ||||
\(688\) | 0.831171 | − | 3.10197i | 0.0316881 | − | 0.118262i | ||||
\(689\) | 21.6322 | + | 12.4894i | 0.824121 | + | 0.475807i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.56231 | −0.363767 | −0.181884 | − | 0.983320i | \(-0.558219\pi\) | ||||
−0.181884 | + | 0.983320i | \(0.558219\pi\) | |||||||
\(692\) | −9.60505 | − | 9.60505i | −0.365129 | − | 0.365129i | ||||
\(693\) | −2.37225 | + | 8.85335i | −0.0901142 | + | 0.336311i | ||||
\(694\) | 25.2411 | + | 43.7188i | 0.958139 | + | 1.65954i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | − | 0.565061i | − | 0.0214186i | ||||||
\(697\) | −0.776457 | + | 2.89778i | −0.0294104 | + | 0.109761i | ||||
\(698\) | −6.36611 | − | 23.7586i | −0.240961 | − | 0.899278i | ||||
\(699\) | −1.73205 | − | 3.00000i | −0.0655122 | − | 0.113470i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.07295 | − | 3.59045i | 0.0782942 | − | 0.135610i | −0.824220 | − | 0.566270i | \(-0.808386\pi\) |
0.902514 | + | 0.430660i | \(0.141719\pi\) | |||||||
\(702\) | 6.55524 | + | 6.55524i | 0.247412 | + | 0.247412i | ||||
\(703\) | −33.1576 | − | 26.2928i | −1.25056 | − | 0.991652i | ||||
\(704\) | − | 24.1033i | − | 0.908428i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −42.6246 | − | 24.6093i | −1.60420 | − | 0.926184i | ||||
\(707\) | −26.2803 | − | 7.04180i | −0.988374 | − | 0.264834i | ||||
\(708\) | 15.7896 | − | 4.23080i | 0.593408 | − | 0.159003i | ||||
\(709\) | 7.90215 | − | 4.56231i | 0.296771 | − | 0.171341i | −0.344220 | − | 0.938889i | \(-0.611857\pi\) |
0.640992 | + | 0.767548i | \(0.278523\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 38.8264i | − | 1.45610i | ||||||
\(712\) | 5.50728 | + | 1.47567i | 0.206394 | + | 0.0553031i | ||||
\(713\) | −7.42499 | − | 1.98952i | −0.278068 | − | 0.0745081i | ||||
\(714\) | − | 0.978714i | − | 0.0366274i | ||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 23.5623 | − | 13.6037i | 0.880565 | − | 0.508394i | ||||
\(717\) | 8.79314 | − | 2.35611i | 0.328386 | − | 0.0879907i | ||||
\(718\) | 66.9102 | + | 17.9285i | 2.49707 | + | 0.669087i | ||||
\(719\) | −33.0169 | − | 19.0623i | −1.23132 | − | 0.710904i | −0.264016 | − | 0.964518i | \(-0.585047\pi\) |
−0.967305 | + | 0.253614i | \(0.918381\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.8151i | 0.626227i | ||||||||
\(722\) | 37.4517 | − | 20.0592i | 1.39381 | − | 0.746525i | ||||
\(723\) | 4.14205 | + | 4.14205i | 0.154044 | + | 0.154044i | ||||
\(724\) | 23.0036 | − | 39.8435i | 0.854923 | − | 1.48077i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.22949 | + | 5.59364i | 0.119858 | + | 0.207599i | ||||
\(727\) | 6.46270 | + | 24.1191i | 0.239688 | + | 0.894529i | 0.975979 | + | 0.217864i | \(0.0699088\pi\) |
−0.736291 | + | 0.676665i | \(0.763425\pi\) | |||||||
\(728\) | −1.85856 | + | 6.93622i | −0.0688826 | + | 0.257074i | ||||
\(729\) | − | 19.4377i | − | 0.719915i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.06231 | − | 1.83997i | −0.0392908 | − | 0.0680537i | ||||
\(732\) | 2.83599 | − | 10.5841i | 0.104821 | − | 0.391198i | ||||
\(733\) | 18.8812 | + | 18.8812i | 0.697392 | + | 0.697392i | 0.963847 | − | 0.266455i | \(-0.0858525\pi\) |
−0.266455 | + | 0.963847i | \(0.585853\pi\) | |||||||
\(734\) | 42.0378 | 1.55164 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −30.1869 | − | 17.4284i | −1.11270 | − | 0.642420i | ||||
\(737\) | −2.87926 | + | 10.7455i | −0.106059 | + | 0.395817i | ||||
\(738\) | 27.9534 | − | 7.49008i | 1.02898 | − | 0.275714i | ||||
\(739\) | 11.2583 | + | 6.50000i | 0.414144 | + | 0.239106i | 0.692569 | − | 0.721352i | \(-0.256479\pi\) |
−0.278425 | + | 0.960458i | \(0.589812\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.354102 | + | 3.06661i | 0.0130083 | + | 0.112655i | ||||
\(742\) | −36.8950 | + | 36.8950i | −1.35446 | + | 1.35446i | ||||
\(743\) | −0.0144235 | − | 0.0538292i | −0.000529147 | − | 0.00197480i | 0.965661 | − | 0.259806i | \(-0.0836587\pi\) |
−0.966190 | + | 0.257832i | \(0.916992\pi\) | |||||||
\(744\) | 0.631757 | − | 1.09424i | 0.0231613 | − | 0.0401166i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −17.0729 | + | 29.5712i | −0.625085 | + | 1.08268i | ||||
\(747\) | 41.1512 | + | 11.0264i | 1.50564 | + | 0.403436i | ||||
\(748\) | −2.60211 | − | 2.60211i | −0.0951425 | − | 0.0951425i | ||||
\(749\) | 1.88823 | 0.0689944 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.6869 | − | 13.0983i | 0.827857 | − | 0.477964i | −0.0252611 | − | 0.999681i | \(-0.508042\pi\) |
0.853118 | + | 0.521717i | \(0.174708\pi\) | |||||||
\(752\) | −2.73861 | + | 2.73861i | −0.0998669 | + | 0.0998669i | ||||
\(753\) | 1.69361 | − | 1.69361i | 0.0617185 | − | 0.0617185i | ||||
\(754\) | −1.37143 | − | 2.37539i | −0.0499446 | − | 0.0865065i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −10.0623 | + | 5.80948i | −0.365963 | + | 0.211289i | ||||
\(757\) | −4.93117 | − | 18.4034i | −0.179226 | − | 0.668881i | −0.995793 | − | 0.0916305i | \(-0.970792\pi\) |
0.816567 | − | 0.577251i | \(-0.195875\pi\) | |||||||
\(758\) | −58.7646 | + | 15.7459i | −2.13443 | + | 0.571918i | ||||
\(759\) | −3.67994 | −0.133573 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.0000 | −0.435000 | −0.217500 | − | 0.976060i | \(-0.569790\pi\) | ||||
−0.217500 | + | 0.976060i | \(0.569790\pi\) | |||||||
\(762\) | −9.53889 | + | 2.55594i | −0.345558 | + | 0.0925919i | ||||
\(763\) | −6.76155 | − | 25.2344i | −0.244784 | − | 0.913548i | ||||
\(764\) | 18.5656 | − | 10.7188i | 0.671679 | − | 0.387794i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 20.0623 | + | 34.7489i | 0.724881 | + | 1.25553i | ||||
\(767\) | 18.7025 | − | 18.7025i | 0.675307 | − | 0.675307i | ||||
\(768\) | 2.43082 | − | 2.43082i | 0.0877145 | − | 0.0877145i | ||||
\(769\) | −2.70599 | + | 1.56231i | −0.0975806 | + | 0.0563382i | −0.547996 | − | 0.836481i | \(-0.684609\pi\) |
0.450416 | + | 0.892819i | \(0.351276\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.85410 | 0.354887 | ||||||||
\(772\) | −17.5896 | − | 17.5896i | −0.633062 | − | 0.633062i | ||||
\(773\) | 49.6771 | + | 13.3110i | 1.78676 | + | 0.478762i | 0.991789 | − | 0.127883i | \(-0.0408181\pi\) |
0.794973 | + | 0.606644i | \(0.207485\pi\) | |||||||
\(774\) | −10.2475 | + | 17.7492i | −0.368339 | + | 0.637983i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 9.57295 | − | 16.5808i | 0.343649 | − | 0.595217i | ||||
\(777\) | 1.66234 | + | 6.20395i | 0.0596362 | + | 0.222565i | ||||
\(778\) | 2.93159 | − | 2.93159i | 0.105103 | − | 0.105103i | ||||
\(779\) | 18.1383 | + | 7.85410i | 0.649871 | + | 0.281402i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.21885 | − | 3.59045i | −0.222528 | − | 0.128477i | ||||
\(782\) | −7.42499 | + | 1.98952i | −0.265517 | + | 0.0711451i | ||||
\(783\) | 0.382883 | − | 1.42894i | 0.0136831 | − | 0.0510662i | ||||
\(784\) | −3.46410 | − | 2.00000i | −0.123718 | − | 0.0714286i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −15.6049 | −0.556608 | ||||||||
\(787\) | −18.4729 | − | 18.4729i | −0.658487 | − | 0.658487i | 0.296535 | − | 0.955022i | \(-0.404169\pi\) |
−0.955022 | + | 0.296535i | \(0.904169\pi\) | |||||||
\(788\) | −1.46613 | + | 5.47167i | −0.0522287 | + | 0.194920i | ||||
\(789\) | −2.47172 | − | 4.28115i | −0.0879957 | − | 0.152413i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 21.3497i | − | 0.759107i | ||||||
\(792\) | −3.06256 | + | 11.4296i | −0.108823 | + | 0.406134i | ||||
\(793\) | −4.58873 | − | 17.1254i | −0.162951 | − | 0.608140i | ||||
\(794\) | −24.6093 | − | 42.6246i | −0.873352 | − | 1.51269i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −31.6869 | + | 54.8834i | −1.12311 | + | 1.94529i | ||||
\(797\) | −27.8473 | − | 27.8473i | −0.986400 | − | 0.986400i | 0.0135084 | − | 0.999909i | \(-0.495700\pi\) |
−0.999909 | + | 0.0135084i | \(0.995700\pi\) | |||||||
\(798\) | −6.37894 | − | 0.943464i | −0.225812 | − | 0.0333983i | ||||
\(799\) | 2.56231i | 0.0906479i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.30244 | + | 3.63871i | 0.222686 | + | 0.128568i | ||||
\(802\) | 58.7646 | + | 15.7459i | 2.07505 | + | 0.556008i | ||||
\(803\) | 21.2612 | − | 5.69693i | 0.750293 | − | 0.201040i | ||||
\(804\) | −5.95426 | + | 3.43769i | −0.209991 | + | 0.121238i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 6.13323i | − | 0.216034i | ||||||
\(807\) | −5.47167 | − | 1.46613i | −0.192612 | − | 0.0516102i | ||||
\(808\) | −33.9278 | − | 9.09092i | −1.19357 | − | 0.319817i | ||||
\(809\) | 35.5623i | 1.25030i | 0.780503 | + | 0.625152i | \(0.214963\pi\) | ||||
−0.780503 | + | 0.625152i | \(0.785037\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.7188 | − | 9.65263i | 0.587078 | − | 0.338950i | −0.176863 | − | 0.984235i | \(-0.556595\pi\) |
0.763941 | + | 0.645286i | \(0.223262\pi\) | |||||||
\(812\) | 3.32056 | − | 0.889741i | 0.116529 | − | 0.0312238i | ||||
\(813\) | 0.207463 | + | 0.0555896i | 0.00727605 | + | 0.00194961i | ||||
\(814\) | 34.8569 | + | 20.1246i | 1.22173 | + | 0.705367i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.252703i | 0.00884637i | ||||||||
\(817\) | −13.0164 | + | 5.15006i | −0.455385 | + | 0.180178i | ||||
\(818\) | −36.7423 | − | 36.7423i | −1.28467 | − | 1.28467i | ||||
\(819\) | −4.58283 | + | 7.93769i | −0.160137 | + | 0.277365i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17.5623 | − | 30.4188i | −0.612929 | − | 1.06162i | −0.990744 | − | 0.135743i | \(-0.956658\pi\) |
0.377815 | − | 0.925881i | \(-0.376675\pi\) | |||||||
\(822\) | 0.856153 | + | 3.19521i | 0.0298618 | + | 0.111446i | ||||
\(823\) | −2.42811 | + | 9.06183i | −0.0846386 | + | 0.315875i | −0.995246 | − | 0.0973981i | \(-0.968948\pi\) |
0.910607 | + | 0.413274i | \(0.135615\pi\) | |||||||
\(824\) | 21.7082i | 0.756241i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 27.6246 | + | 47.8472i | 0.961183 | + | 1.66482i | ||||
\(827\) | −4.67317 | + | 17.4405i | −0.162502 | + | 0.606465i | 0.835844 | + | 0.548967i | \(0.184979\pi\) |
−0.998346 | + | 0.0574979i | \(0.981688\pi\) | |||||||
\(828\) | 31.4599 | + | 31.4599i | 1.09331 | + | 1.09331i | ||||
\(829\) | −51.9247 | −1.80342 | −0.901709 | − | 0.432344i | \(-0.857687\pi\) | ||||
−0.901709 | + | 0.432344i | \(0.857687\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.16718 | + | 5.29268i | 0.318006 | + | 0.183601i | ||||
\(832\) | 6.23840 | − | 23.2820i | 0.216278 | − | 0.807159i | ||||
\(833\) | −2.55617 | + | 0.684923i | −0.0885659 | + | 0.0237312i | ||||
\(834\) | 1.80310 | + | 1.04102i | 0.0624362 | + | 0.0360476i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −19.4681 | + | 14.4513i | −0.673317 | + | 0.499808i | ||||
\(837\) | 2.33905 | − | 2.33905i | 0.0808496 | − | 0.0808496i | ||||
\(838\) | 18.1818 | + | 67.8555i | 0.628081 | + | 2.34403i | ||||
\(839\) | 15.9192 | − | 27.5729i | 0.549594 | − | 0.951924i | −0.448709 | − | 0.893678i | \(-0.648116\pi\) |
0.998302 | − | 0.0582459i | \(-0.0185507\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.2812 | − | 24.7357i | 0.492454 | − | 0.852955i | ||||
\(842\) | −72.6371 | − | 19.4630i | −2.50324 | − | 0.670741i | ||||
\(843\) | 1.40343 | + | 1.40343i | 0.0483368 | + | 0.0483368i | ||||
\(844\) | −54.8834 | −1.88916 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 21.4058 | − | 12.3586i | 0.735945 | − | 0.424898i | ||||
\(847\) | −9.26190 | + | 9.26190i | −0.318242 | + | 0.318242i | ||||
\(848\) | 9.52624 | − | 9.52624i | 0.327132 | − | 0.327132i | ||||
\(849\) | −6.04374 | − | 10.4681i | −0.207421 | − | 0.359263i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 43.6869 | − | 25.2227i | 1.49757 | − | 0.864621i | ||||
\(852\) | −1.14865 | − | 4.28682i | −0.0393521 | − | 0.146864i | ||||
\(853\) | −36.0744 | + | 9.66612i | −1.23517 | + | 0.330962i | −0.816589 | − | 0.577220i | \(-0.804138\pi\) |
−0.418577 | + | 0.908181i | \(0.637471\pi\) | |||||||
\(854\) | 37.0347 | 1.26730 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.43769 | 0.0833187 | ||||||||
\(857\) | 32.6135 | − | 8.73875i | 1.11405 | − | 0.298510i | 0.345579 | − | 0.938390i | \(-0.387682\pi\) |
0.768475 | + | 0.639880i | \(0.221016\pi\) | |||||||
\(858\) | −0.759929 | − | 2.83609i | −0.0259436 | − | 0.0968227i | ||||
\(859\) | −35.1280 | + | 20.2812i | −1.19855 | + | 0.691984i | −0.960232 | − | 0.279203i | \(-0.909930\pi\) |
−0.238319 | + | 0.971187i | \(0.576596\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.50000 | − | 2.59808i | −0.0511199 | − | 0.0885422i | ||||
\(862\) | −40.0331 | + | 40.0331i | −1.36353 | + | 1.36353i | ||||
\(863\) | 26.9188 | − | 26.9188i | 0.916325 | − | 0.916325i | −0.0804345 | − | 0.996760i | \(-0.525631\pi\) |
0.996760 | + | 0.0804345i | \(0.0256308\pi\) | |||||||
\(864\) | 12.9904 | − | 7.50000i | 0.441942 | − | 0.255155i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 31.5836 | 1.07325 | ||||||||
\(867\) | −4.47333 | − | 4.47333i | −0.151922 | − | 0.151922i | ||||
\(868\) | 7.42499 | + | 1.98952i | 0.252021 | + | 0.0675287i | ||||
\(869\) | −12.6113 | + | 21.8435i | −0.427810 | + | 0.740989i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.56231 | + | 9.63420i | −0.188472 | + | 0.326442i | ||||
\(872\) | −8.72912 | − | 32.5775i | −0.295605 | − | 1.10321i | ||||
\(873\) | 17.2801 | − | 17.2801i | 0.584841 | − | 0.584841i | ||||
\(874\) | 5.80948 | + | 50.3115i | 0.196508 | + | 1.70181i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 11.7812 | + | 6.80185i | 0.398048 | + | 0.229813i | ||||
\(877\) | 2.05222 | − | 0.549890i | 0.0692985 | − | 0.0185685i | −0.224003 | − | 0.974588i | \(-0.571913\pi\) |
0.293302 | + | 0.956020i | \(0.405246\pi\) | |||||||
\(878\) | 14.7435 | − | 55.0236i | 0.497570 | − | 1.85696i | ||||
\(879\) | −1.87684 | − | 1.08359i | −0.0633041 | − | 0.0365487i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.5623 | 1.50134 | 0.750671 | − | 0.660676i | \(-0.229730\pi\) | ||||
0.750671 | + | 0.660676i | \(0.229730\pi\) | |||||||
\(882\) | 18.0509 | + | 18.0509i | 0.607806 | + | 0.607806i | ||||
\(883\) | −4.48288 | + | 16.7303i | −0.150861 | + | 0.563020i | 0.848563 | + | 0.529094i | \(0.177468\pi\) |
−0.999424 | + | 0.0339267i | \(0.989199\pi\) | |||||||
\(884\) | −1.83997 | − | 3.18692i | −0.0618848 | − | 0.107188i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 72.6724i | 2.44148i | ||||||||
\(887\) | 4.96975 | − | 18.5473i | 0.166868 | − | 0.622759i | −0.830927 | − | 0.556382i | \(-0.812189\pi\) |
0.997795 | − | 0.0663773i | \(-0.0211441\pi\) | |||||||
\(888\) | 2.14607 | + | 8.00926i | 0.0720176 | + | 0.268773i | ||||
\(889\) | −10.0133 | − | 17.3435i | −0.335834 | − | 0.581681i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.14590 | + | 12.3771i | −0.239397 | + | 0.414647i | ||||
\(892\) | 35.7529 | + | 35.7529i | 1.19710 | + | 1.19710i | ||||
\(893\) | 16.7003 | + | 2.47002i | 0.558853 | + | 0.0826561i | ||||
\(894\) | 8.29180i | 0.277319i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 23.4787 | + | 13.5554i | 0.784369 | + | 0.452856i | ||||
\(897\) | −3.55454 | − | 0.952437i | −0.118683 | − | 0.0318010i | ||||
\(898\) | −30.8113 | + | 8.25585i | −1.02818 | + | 0.275501i | ||||
\(899\) | −0.847591 | + | 0.489357i | −0.0282687 | + | 0.0163210i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 8.91296i | − | 0.296934i | ||||||
\(902\) | −18.1593 | − | 4.86576i | −0.604637 | − | 0.162012i | ||||
\(903\) | 2.05222 | + | 0.549890i | 0.0682935 | + | 0.0182992i | ||||
\(904\) | − | 27.5623i | − | 0.916709i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3.46962 | + | 2.00319i | −0.115271 | + | 0.0665515i | ||||
\(907\) | 22.0754 | − | 5.91508i | 0.733001 | − | 0.196407i | 0.127035 | − | 0.991898i | \(-0.459454\pi\) |
0.605965 | + | 0.795491i | \(0.292787\pi\) | |||||||
\(908\) | −39.0393 | − | 10.4605i | −1.29556 | − | 0.347145i | ||||
\(909\) | −38.8264 | − | 22.4164i | −1.28779 | − | 0.743505i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 13.0386i | − | 0.431990i | −0.976395 | − | 0.215995i | \(-0.930701\pi\) | ||
0.976395 | − | 0.215995i | \(-0.0692994\pi\) | |||||||
\(912\) | 1.64703 | + | 0.243601i | 0.0545387 | + | 0.00806644i | ||||
\(913\) | −19.5698 | − | 19.5698i | −0.647667 | − | 0.647667i | ||||
\(914\) | −38.1648 | + | 66.1033i | −1.26238 | + | 2.18650i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16.5000 | − | 28.5788i | −0.545175 | − | 0.944271i | ||||
\(917\) | −8.19045 | − | 30.5672i | −0.270472 | − | 1.00942i | ||||
\(918\) | 0.856153 | − | 3.19521i | 0.0282573 | − | 0.105458i | ||||
\(919\) | 46.5623i | 1.53595i | 0.640481 | + | 0.767974i | \(0.278735\pi\) | ||||
−0.640481 | + | 0.767974i | \(0.721265\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.57295 | − | 6.18853i | −0.117733 | − | 0.203919i | ||||
\(922\) | −1.98952 | + | 7.42499i | −0.0655214 | + | 0.244529i | ||||
\(923\) | −5.07767 | − | 5.07767i | −0.167133 | − | 0.167133i | ||||
\(924\) | 3.67994 | 0.121061 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −48.8435 | − | 28.1998i | −1.60510 | − | 0.926702i | ||||
\(927\) | −7.17141 | + | 26.7641i | −0.235540 | + | 0.879047i | ||||
\(928\) | −4.28682 | + | 1.14865i | −0.140722 | + | 0.0377063i | ||||
\(929\) | 33.3959 | + | 19.2812i | 1.09569 | + | 0.632594i | 0.935084 | − | 0.354425i | \(-0.115323\pi\) |
0.160601 | + | 0.987019i | \(0.448657\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.00000 | + | 17.3205i | 0.0655474 | + | 0.567657i | ||||
\(932\) | 19.2385 | − | 19.2385i | 0.630179 | − | 0.630179i | ||||
\(933\) | 0.889741 | + | 3.32056i | 0.0291288 | + | 0.108710i | ||||
\(934\) | −5.70156 | + | 9.87539i | −0.186561 | + | 0.323133i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.91641 | + | 10.2475i | −0.193384 | + | 0.334951i | ||||
\(937\) | 30.3587 | + | 8.13458i | 0.991775 | + | 0.265745i | 0.717996 | − | 0.696047i | \(-0.245060\pi\) |
0.273779 | + | 0.961793i | \(0.411726\pi\) | |||||||
\(938\) | −16.4317 | − | 16.4317i | −0.536513 | − | 0.536513i | ||||
\(939\) | −4.43804 | −0.144830 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.62461 | − | 3.82472i | 0.215956 | − | 0.124682i | −0.388120 | − | 0.921609i | \(-0.626875\pi\) |
0.604076 | + | 0.796926i | \(0.293542\pi\) | |||||||
\(942\) | 0.893439 | − | 0.893439i | 0.0291098 | − | 0.0291098i | ||||
\(943\) | −16.6611 | + | 16.6611i | −0.542559 | + | 0.542559i | ||||
\(944\) | −7.13264 | − | 12.3541i | −0.232148 | − | 0.402092i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11.5304 | − | 6.65707i | 0.374885 | − | 0.216440i | ||||
\(947\) | −10.6840 | − | 39.8731i | −0.347182 | − | 1.29570i | −0.890042 | − | 0.455878i | \(-0.849325\pi\) |
0.542860 | − | 0.839823i | \(-0.317341\pi\) | |||||||
\(948\) | −15.0573 | + | 4.03459i | −0.489038 | + | 0.131037i | ||||
\(949\) | 22.0113 | 0.714516 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.83282 | −0.221569 | ||||||||
\(952\) | 2.47500 | − | 0.663174i | 0.0802151 | − | 0.0214936i | ||||
\(953\) | −9.59964 | − | 35.8264i | −0.310963 | − | 1.16053i | −0.927690 | − | 0.373352i | \(-0.878208\pi\) |
0.616727 | − | 0.787177i | \(-0.288458\pi\) | |||||||
\(954\) | −74.4598 | + | 42.9894i | −2.41072 | + | 1.39183i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 35.7492 | + | 61.9195i | 1.15621 | + | 2.00262i | ||||
\(957\) | −0.331306 | + | 0.331306i | −0.0107096 | + | 0.0107096i | ||||
\(958\) | −41.3066 | + | 41.3066i | −1.33456 | + | 1.33456i | ||||
\(959\) | −5.80948 | + | 3.35410i | −0.187598 | + | 0.108310i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.8115 | 0.929404 | ||||||||
\(962\) | 28.4605 | + | 28.4605i | 0.917603 | + | 0.917603i | ||||
\(963\) | 3.00544 | + | 0.805304i | 0.0968488 | + | 0.0259506i | ||||
\(964\) | −23.0036 | + | 39.8435i | −0.740897 | + | 1.28327i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.84346 | − | 6.65707i | 0.123661 | − | 0.214188i | ||||
\(967\) | 0.896575 | + | 3.34607i | 0.0288319 | + | 0.107602i | 0.978842 | − | 0.204616i | \(-0.0655946\pi\) |
−0.950010 | + | 0.312218i | \(0.898928\pi\) | |||||||
\(968\) | −11.9571 | + | 11.9571i | −0.384314 | + | 0.384314i | ||||
\(969\) | 0.884460 | − | 0.656541i | 0.0284129 | − | 0.0210911i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.64590 | − | 3.25966i | −0.181185 | − | 0.104607i | 0.406664 | − | 0.913578i | \(-0.366692\pi\) |
−0.587850 | + | 0.808970i | \(0.700025\pi\) | |||||||
\(972\) | −27.9707 | + | 7.49473i | −0.897161 | + | 0.240394i | ||||
\(973\) | −1.09279 | + | 4.07834i | −0.0350332 | + | 0.130746i | ||||
\(974\) | −50.5901 | − | 29.2082i | −1.62101 | − | 0.935891i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.56231 | −0.306082 | ||||||||
\(977\) | 43.5404 | + | 43.5404i | 1.39298 | + | 1.39298i | 0.818559 | + | 0.574423i | \(0.194774\pi\) |
0.574423 | + | 0.818559i | \(0.305226\pi\) | |||||||
\(978\) | −0.382883 | + | 1.42894i | −0.0122433 | + | 0.0456925i | ||||
\(979\) | −2.36381 | − | 4.09424i | −0.0755476 | − | 0.130852i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 43.0486i | − | 1.37443i | ||||||
\(982\) | −4.70201 | + | 17.5482i | −0.150047 | + | 0.559984i | ||||
\(983\) | −8.69548 | − | 32.4520i | −0.277343 | − | 1.03506i | −0.954255 | − | 0.298993i | \(-0.903349\pi\) |
0.676912 | − | 0.736064i | \(-0.263318\pi\) | |||||||
\(984\) | −1.93649 | − | 3.35410i | −0.0617331 | − | 0.106925i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.489357 | + | 0.847591i | −0.0155843 | + | 0.0269928i | ||||
\(987\) | −1.81182 | − | 1.81182i | −0.0576710 | − | 0.0576710i | ||||
\(988\) | −22.5450 | + | 8.92017i | −0.717251 | + | 0.283788i | ||||
\(989\) | − | 16.6869i | − | 0.530613i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.3435 | − | 6.54915i | −0.360337 | − | 0.208041i | 0.308892 | − | 0.951097i | \(-0.400042\pi\) |
−0.669229 | + | 0.743057i | \(0.733375\pi\) | |||||||
\(992\) | −9.58562 | − | 2.56846i | −0.304344 | − | 0.0815487i | ||||
\(993\) | 3.83425 | − | 1.02738i | 0.121676 | − | 0.0326030i | ||||
\(994\) | 12.9904 | − | 7.50000i | 0.412030 | − | 0.237886i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 17.1047i | − | 0.541982i | ||||||
\(997\) | −53.7455 | − | 14.4011i | −1.70214 | − | 0.456086i | −0.728661 | − | 0.684874i | \(-0.759857\pi\) |
−0.973476 | + | 0.228788i | \(0.926524\pi\) | |||||||
\(998\) | 65.0654 | + | 17.4342i | 2.05961 | + | 0.551871i | ||||
\(999\) | 21.7082i | 0.686817i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 475.2.p.g.293.3 | yes | 16 | |
5.2 | odd | 4 | inner | 475.2.p.g.407.3 | yes | 16 | |
5.3 | odd | 4 | inner | 475.2.p.g.407.2 | yes | 16 | |
5.4 | even | 2 | inner | 475.2.p.g.293.2 | yes | 16 | |
19.12 | odd | 6 | inner | 475.2.p.g.468.3 | yes | 16 | |
95.12 | even | 12 | inner | 475.2.p.g.107.3 | yes | 16 | |
95.69 | odd | 6 | inner | 475.2.p.g.468.2 | yes | 16 | |
95.88 | even | 12 | inner | 475.2.p.g.107.2 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
475.2.p.g.107.2 | ✓ | 16 | 95.88 | even | 12 | inner | |
475.2.p.g.107.3 | yes | 16 | 95.12 | even | 12 | inner | |
475.2.p.g.293.2 | yes | 16 | 5.4 | even | 2 | inner | |
475.2.p.g.293.3 | yes | 16 | 1.1 | even | 1 | trivial | |
475.2.p.g.407.2 | yes | 16 | 5.3 | odd | 4 | inner | |
475.2.p.g.407.3 | yes | 16 | 5.2 | odd | 4 | inner | |
475.2.p.g.468.2 | yes | 16 | 95.69 | odd | 6 | inner | |
475.2.p.g.468.3 | yes | 16 | 19.12 | odd | 6 | inner |